Nodal Analysis

• Mesh Analysis for Current
• Used to calculate all node Voltages in a Circuits
  • This is a voltage between a node and a "reference node"
• Useful when reducing to series/parallel is not possible

1. Use Kirchhoff's Laws#Current at every node except the reference node to get a system of equations
   • You can replace the currents with $\frac{\mathrm{\Delta }V}{R}$, where $\mathrm{\Delta }V$ is the difference in node voltages across a path
     • Just make sure you're subtracting from higher to lower voltage, based on how you defined the current direction
   • You can also skip grounded voltage sources
2. Solve to get node voltages

• We can simplify a floating voltage source by creating a "supernode"
  • Enclose the source and its terminals, along with any parallel elements in a dotted line
  • Now you can do Kirchhoff's Laws#Current as though the supernode were a node, in the sense that the current will be the same across the whole thing, so you can use the same KCL equation
    • ie, just combine the KCL equations of the individual nodes
    • you remove one equation, but you get another back due to you having the difference between the voltages
    • Note that this does not mean the nodal voltages are equal